LOS ANGELES — A quartet of all-time guards got one step closer to basketball immortality on Saturday, as the Naismith Memorial Basketball Hall of Fame announced that two-time NBA Most Valuable Player Steve Nash, two-time NBA champion Ray Allen, 10-time NBA All-Star Jason Kidd and seven-time All-Star Grant Hill all made the list of finalists for enshrinement in the Hall’s class of 2018.

Nash, Allen, Kidd and Hill are all making their first appearance on the Hall of Fame ballot, made possible by a shift in Hall policy announced in December that sped up the process for potential honorees to come up for consideration. In the past, they needed to be retired for five full years to be eligible; now, you can hit the ballot after three years, allowing Nash and Allen (both of whom last played in 2014) to join Kidd and Hill (who last played in 2013) in this year’s player pool.

Nash led the NBA in total assists six times in an eight-year span between 2004 and 2012 as the pilot of the run-and-gun Phoenix Suns, whose “Seven Seconds or Less” attack helped revolutionize offense in the NBA. He stands as one of only 13 players in league history to win multiple Most Valuable Player awards, joining Hall of Famers Kareem Abdul-Jabbar, Bill Russell, Michael Jordan, Wilt Chamberlain, Moses Malone, Larry Bird, Magic Johnson, Bob Pettit and Karl Malone, as well as three others — Tim Duncan, LeBron James and Stephen Curry — certain to earn enshrinement as soon as they’re eligible.

No player in NBA history has made more 3-pointers than Allen, who was a dominant all-court scorer for the Seattle SuperSonics and Milwaukee Bucks early in his career, and an All-Star-level producer for the Boston Celtics team that won the 2008 NBA title, before settling into a role as a designated sniper for the Miami Heat. His shot to extend Game 6 of the 2013 NBA Finals, allowing the Heat to live another day and eventually take down the San Antonio Spurs in Game 7, stands as perhaps the greatest clutch shot in NBA history.

Marked for superstardom after a pair of NCAA titles at Duke, Hill was a prototypical do-everything swingman for the Detroit Pistons and an All-Star selection in five of his first six NBA seasons before injuries began to derail his career in 2000. But despite spending the bulk of the next four seasons on the shelf, Hill persevered, making the difficult mid-career adjustment from former star to roleplayer and fashioning a dynamite second act as a complimentary player in Orlando and Phoenix.

Few players in recent NBA history have been better able to control all facets of a game than Kidd, a regular among the league leaders on both the assists and steals lists. Kidd made nine All-Defensive Team appearances, earned six All-NBA selections and led the league in assists five times, helping transform the late-’90s Phoenix Suns and early-2000s New Jersey Nets into perennial playoff squads. Like Kidd, he too made a late-career adjustment, developing into a reliable 3-point shooter and steady hand on the ball to help lead the Dallas Mavericks to the 2011 NBA championship. He left the court in 2013 and moved right to the bench as a head coach, first for the Brooklyn Nets, and then for the Milwaukee Bucks, before being fired earlier this year.

They’re joined among first-timers by a pair of greats from the world of women’s basketball: Katie Smith, who won gold medals with Team USA in 2000, 2004 and 2008, as well as a pair of WNBA championships with the Detroit Shock during a decorated playing career before becoming a coach with the New York Liberty; and Tina Thompson, the first draft pick in the history of the WNBA, a four-time WNBA champion with the Houston Comets, and a two-time gold medalist with Team USA.

Nash, Allen, Kidd and Hill are also joined by several NBA luminaries who have previously appeared on the ballot but fallen short of enshrinement: four-time All-Star guard and current Oklahoma City Thunder assistant coach Maurice Cheeks, five-time All-Star Chris Webber, and Rudy Tomjanovich, who coached the Houston Rockets to back-to-back titles in 1994 and 1995.

Rounding out the list of finalists forwarded by the Hall’s North American and Women’s screening Committees:

• Charles “Lefty” Driesell: The only coach in NCAA history to win 100 games at four different schools, one of just four coaches to lead four schools to the NCAA Tournament, and the only coach in NCAA history to be named Conference Coach of the Year in four different conferences; eighth among Division I coaches in all-time victories with an overall coaching record of 786-394 (.666);

• Wayland Baptist University: Coached by Hall of Fame nominee Harley Redin, the Wayland Baptist University women’s basketball team won 131 consecutive games between 1953 and 58 and 10 AAU National Championships.

• Kim Mulkey, the two-time NCAA championship-winning head coach of Baylor University’s women’s basketball team, who has led the Bears to 16 NCAA Tournament appearances, 12 Sweet Sixteens, eight Elite Eights and three Final Fours, and who stands alone as the first person to win a national championship as a player, assistant coach and head coach.

North American and Women’s Committee finalists need 18 of 24 votes from the Honors Committee for election into the Naismith Memorial Basketball Hall of Fame. Those who make the cut will join enshrinees from the “direct-elect” Early African-American Pioneers, International, Contributors and Veterans Committees announced on Saturday, March 31, at a press conference in San Antonio prior to the NCAA Men’s Championship game. The Class of 2018 will be enshrined in Springfield during the weekend of Sept. 6-8, 2018.